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JOURNAL OF THE ATMOSPHERIC SCIENCES, 60, 1881-1894, 2003
Monte Carlo simulation of solar reflectances for cloudy atmospheres
H. W. Barker, R. K. Goldstein, D. E. Stevens
Abstract
Monte Carlo simulations of solar radiative transfer were performed for a well-resolved, large, three-dimensional
(3D) domain of boundary layer cloud simulated by a cloud-resolving model. In order to represent 3D distributions
of optical properties for; 2 3 106 cloudy cells, attenuation by droplets was handled by assigning each cell a
cumulative distribution of extinction derived from either a model or an assumed discrete droplet size spectrum.
This minimizes the required number of detailed phase functions. Likewise, to simulate statistically significant,
high-resolution imagery, it was necessary to apply variance reduction techniques. Three techniques were developed
for use with the local estimation method of computing reflectance rho. First, small fractions of rho come from numerous,
small contributions of zeta computed at each scattering event. Terminating calculation of zeta when it falls below zeta(min)
approximate to 10(-3) was found to impact estimates of rho minimally but reduced computation time by similar to10%.
Second, large fractions of rho come from infrequent realizations of large zeta. When sampled poorly, they boost
Monte Carlo noise significantly. Removing zeta - zeta(max), storing them in a domainwide reservoir, adding zeta(max)
to local estimates of rho, and, at simulation's end, distributing the reservoir across the domain in proportion to local rho,
tends to reduce variance much. This regionalization technique works well when the number of photons per unit area is small
( nominally less than or similar to 50 000). A value of zeta(max) approximate to 100 reduces variance of rho greatly with
little impact on estimates of rho. Third, if zeta are computed using exact (e.g., Mie) phase functions for the first N scattering
events, and thereafter a blunt-nosed corresponding phase function (e.g., Henyey-Greenstein) is used, production of
large zeta is thwarted resulting in reduced variance and time required to achieve accurate estimates of rho.
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